Jewish prophecies speak about the Gentiles (and their blessing of eternal life), but they speak to the Jews, through whom salvation came to the Gentiles (Rom 11:11).
In my opinion, establishing the basis for the concept concerning the distinctions between Israel and the Church could be in how one defines "the new testament (covenant) in My blood" (Luke 22:20). It is my present understanding that the new covenant in Christ's blood is a covenant which is not between man and God, as the Decalogue (Ten Commandments) was with the nation Israel. It is a covenant between the Father and the Son (made in eternity, before creation), of which man is only a recipient ("everlasting covenant" - Heb 13:20, 21). I believe this covenant has been accurately summed up in the concept that the Father would raise His Son from the dead when He died to atone for sin in believers.
Thus, when the Lord Jesus was revealing it to the Jews (who are first in everything spiritual), the word "new" designed a dual intention concerning chronologically and application: chronologically "new" because it had yet to be brought forth in time, and "new", in that it was different from the old (old--conditional; new--unconditional).
To the Gentile, "new" designs a single intention concerning chronology only, because the Gentile never has and never will need to enter a covenant between them and God, but has entered the covenant between the Father and the Son (Everlasting Covenant), same now as the believing Jew.
The Millennium Jew (Jews who have yet to believe in Jesus) new covenant will also be everlasting (same as the believing Christian Jew) and will not be as the old covenant (Jer 31:32), where they could not avoid "braking" it (also v 32), because it requires God "causing" (Eze 36:27) them to keep His statutes and laws--through putting His Spirit in them (again Eze 36:27), same as Christians (Jew/Gentile) now (Gal 5:17).
This concept has other implications that I'm still researching to understand, which may be resolved as we continue to share with one another and correspond with what the Lord gives us to use. I would rather learn and accept a truth that may conflict with my present understanding concerning Scripture doctrine, than to worry about being embarrassed from not having an explanation for a concept or belief. One of my motives for sharing my beliefs is to as much as possible, learn truth, because the Spirit teaches through us all.
I've been sharing that Abraham is the father of faith as in first in the faith of God's grace, making him the father of the faith among the believing world. Similar concept to John 8:44 concerning the Enemy. "What was written in the books of the Old Testament, was not written merely on account of them who are the subjects thereof, but for the use, learning, instruction and profit of saints under the New Testament dispensation" JG (But for us also - Rom 4:24).
It may have been noticed that I often use John Gill's commentary but I want it to be known that at present, my dispensational concepts do not always parallel his because at times he spiritualizes, as many do, Israel (unbelieving Jews, which will be the majority of Israel until later) to be the Church.
At present, I can see that Abraham becomes the father of the believing Gentile as in a spiritual-mystical sense concerning the faith in God, but as yet I fail to see how this is to support the concept that the Church is Israel.
It will help for me to explain that I have the understanding that there will be unbelieving Jews saved later (living Jews who make up Israel at that time), who will be the ones to "inherit the earth." The companion-concept to Israel inheriting the "new earth" is, that when Scripture speaks of saints dwelling in Heaven, these are those who believed before they died and before Jesus returns.
This is why I still fail to comprehend that Ezekiel 36 and Jeremiah 31 are in any reference to Gentiles, considering the ominous Jewish-posterity usage, which appears to explain that the new covenant of Israel indicated in Jer/Eze prophecies are similar to the new covenant which has been since Christ's ascension, e.g. Spirit given and God causing them to walk in statues and laws. This Israelite covenant would be the result of new covenant in His blood, as is the present Christian new covenant, which is the "everlasting covenant" (Heb 13:20,21); but the two would not be "blessed" (John 20:29) the same (saved Israel--new earth; saved Christian--new heaven?).
I encountered these concepts (Israel/Church distinctions and eternal states) about ten years ago and I still find that there is a good possibility of them being true. I haven't exhausted the comprehensive input Scripture has concerning them, nor have I come to the understanding that the Spirit has shown me a confirmation as to accept them as speculation or truth. It's all in the patience of waiting on the Lord!